Why pour money into a building of little architectural merit just because it is old? There are many better and more interesting buildings that are worth more attention. The same applies to churches, incidentally. Some are of very little merit. Others are breathtaking gems.
Everybody seems to have got their knickers well and truly twisted in this thread.
Back to first principles. Sriram talks about the queen getting a pay rise. He lives a long way away and there is no reason why he should be aware of how the monarchy is funded. It does not come out of government expenditure - except in a roundabout way. George V (I believe) came to an arrangement with the government. All Crown property should be merged into the Crown Estate and the costs of the monarchy would be funded from the Crown Estate not the Treasury. So the monarchy is not paid for out of taxation.
Last year, the Crown Estate had a surplus of about £300million. This not just from Scottish castles and their farms but commercial property management (Regents Street, apparently, is owned by the Crown Estate as is a shopping arcade in Worcester). The costs of running the monarchy are taken from this surplus and the remainder given to the Treasury. All that this "pay rise" amounts to is that the amount given to the Treasury is about £5million less than would otherwise have been the case.
The fact that the money is being spent on modernising a rather dowdy building at the bottom end of The Mall should be of little interest to taxpayers because it hasn't come from collected taxes. OK, Treasury income would have been a little higher otherwise, but then so it might be after the ultimate stupidity of Brexit had resulted in wholesale insolvency in flagship London shops.